Abstract In our teaching approach to quantum mechanics for high schools, we combined a two-state system approach with a matter-wave approach. We developed a simulation of a double well, which has been gradually improved with experience to include all the functionality needed to address the most important concepts of quantum physics. A complementary simulation of a double slit has also been developed to address the introduction of the wave function. A course, based on these simulations has been developed and is currently being tested for the fourth year, still undergoing improvements. Each year a series of formative questions and a pre- and post-test has been administered. We report here how the simulation is used to address the concepts of quantum physics and some preliminary results from the ongoing study of the course.
Abstract In our teaching approach to quantum mechanics for high schools, we combined a two-state system approach with a matter-wave approach. We developed a simulation of a double well, which has been gradually improved with experience to include all the functionality needed to address the most important concepts of quantum physics. A complementary simulation of a double slit has also been developed to address the introduction of the wave function. A course, based on these simulations has been developed and is currently being tested for the fourth year, still undergoing improvements. Each year a series of formative questions and a pre- and post-test has been administered. We report here how the simulation is used to address the concepts of quantum physics and some preliminary results from the ongoing study of the course.
Abstract Teaching introductory quantum mechanics is challenging, especially to students who have limited knowledge of mathematics. The challenges and approaches are evidenced in a wide range of literature. Our goal is to develop an active engagement module for introductory quantum mechanics that would cover the most important concepts: indeterminism, incompatibility, the difference between superposition and statistical mixture and the role of measurement. To accomplish this, we developed a free on-line simulation of a double well—a (pseudo) two-state system—which is able to evidence all of the above concepts. Students perform simulated experiments and build their knowledge from their observations. We present the simulation and the proposed experiments to address the above concepts. We provide a description of the activities and their outcomes as tested with high-school students in different settings. Qualitative analysis of learning outcomes offers evidence that between 60% and 100% of students can reach the following conclusions on their own. (i) The particle is only ever detected in one of the possible states. (ii) The outcome of one experiment cannot be predicted, only its probability can be predicted. (iii) For some pairs of quantities, knowing the value of one quantity exactly precludes the possibility of knowing the value of the other quantity exactly. (iv) A statistical mixture (of eigenstates) is not the same as a superposition state. (v) The measurement affects the time evolution of the system. The most difficult conclusion for students to reach is how exactly the measurement affects the system. The success rates presented here lead us to conclude that the simulated experiments can be very useful when designing an active engagement course on the concepts of quantum mechanics. While the development is done in high-school, we believe the results are also relevant for introductory university level, especially for non-physics students.
Teaching quantum mechanics at the secondary school level remains a major educational challenge. Traditional historical approaches often present the theory as a sequence of disconnected phenomena, requiring extensive prior knowledge of classical physics before students can appreciate the conceptual structure of quantum physics. In this work, we present the design, implementation, and evaluation of a curriculum based on the two state (qubit first) approach, in which the fundamental postulates of quantum mechanics are introduced through mathematically accessible two level systems and realized with light polarization. The curriculum integrates theoretical instruction, laboratory activities, a coherent progression grounded in the interactive simulations, and inquiry based learning into a coherent pathway that progresses from quantum states and superposition to entanglement and the experimental violation of Bell's inequalities. A distinctive feature of the project is the experimental realization of the violation of Bell's inequalities obtained in a newly established quantum optics laboratory in an Italian high school, where students performed, for the first time in Italy, an authentic Bell test using polarization-entangled photons. The same educational framework was adopted for in service teacher professional development courses. Learning outcomes were evaluated through mixed methods. Preliminary analysis indicates significant improvements in conceptual understanding, confidence in using mathematical formalism, and appreciation of the relationship between theory, experimentation, and the foundations of quantum mechanics. The proposed curriculum shows that two-state formalism and supported by real laboratory experiences enables secondary-school students to engage more meaningfully with both the conceptual foundations of quantum mechanics and their experimental verification.
Abstract Teaching and learning quantum mechanics is one of the most demanding educational and conceptual challenges, in particular in secondary schools where students do not possess an adequate mathematical background to effectively support the description of quantum behaviour. Educational research shows that traditional approaches, generally based on historical and narrative perspectives, are only partially effective. The reason is that they do not address in depth those basic quantum concepts that radically question the fundamentals of classical physics. A research-based educational program has been proposed to two final-year classes of an Italian scientific high school. In order to build the main concepts of quantum mechanics and their formal basic representation via real and simulated experiments, the program uses the light polarization as a context. A quantum game was then integrated in the educational program, to support students’ learning. Their conceptual paths, monitored by means of tutorials and questionnaires, show significant student learning especially on the concept of state and on appropriating the formalism meaning, whereas students more frequently referred to the geometrical vector representation instead of the algebraic-analytic formula. The quantum game has emerged to support intuition and operative experience in distinguishing the foundational concepts of superposition and entanglement.
In this paper we present a proposal for teaching basic aspects of quantum mechanics in high school. Our proposal is based on a wave approach that makes use of the analogies between wave phenomena at macroscopic scales and phenomena at atomic or subatomic scales. Although the classical and the quantum model are completely different, there is a common underlying wave mathematical layer. This allows to address, via analogies, quantum aspects that are not accessible to direct experience. The quantization of energy levels, the quantum interference and the uncertainty relations are examples of quantum aspects having an analog concept in classical physics wave phenomena. In our approach we break the wave-particle “duality”, which is totally counterintuitive. Instead we enhance the underlying wave mathematical structure as a path to reach and explain emerging features of particles and quantum systems in general.
[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] The teaching and learning of quantum physics has recently become a topic of increasing interest in physics education research. In particular, the study of two-state systems is gaining importance as a means of teaching quantum physics at various educational levels. Meanwhile, a number of approaches have been developed that are also suitable for high school students. It can be assumed that the different approaches have different degrees of effectiveness in teaching central quantum concepts. However, suitable evaluation instruments to test this are still lacking. Therefore, as a first step, a short questionnaire on quantum measurement, suitable for both research and classroom use, was developed in several steps. First, a questionnaire with open and closed items was created and piloted with a total of N = 120 learners. The responses were evaluated qualitatively using a comprehensive coding manual, which provided insights into learners’ conceptions. These results led to the development of an eight-item questionnaire that could be adapted to different teaching approaches. This questionnaire was subjected to expert review and, finally, successfully tested for its psychometric properties with a sample of N = 201 learners. Overall, our results provide initial empirical evidence that context (i.e., which two-state approach is used) does matter for student learning, but in general, two-state approaches appear to be particularly conducive to learning quantum concepts (specified in this article for quantum measurement) compared to traditional instruction. Published by the American Physical Society 2024
Quantum mechanics is one of the most challenging subjects to learn. It is challenging because quantum phenomenon is counterintuitive, and the mathematics used to explain such a phenomenon is very abstract, and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas step- by- step in a structured way with a comparison between quantum and classical concepts. It provides a clear distinction between classical and quantum logic. Conceptual questions are provided after every important section so that the reader can test their understanding at every step. Such an approach aids in preventing misconceptions. Problem solving is not restricted to solving differential equations and integration. But it requires to systematically and creatively analyze a problem, to apply the new and powerful concepts for finding a solution and to understand the physical meaning of the solution. The tutorials on special topics are an effort to teach problem solving by actively engaging the reader in a thinking process, to apply the concepts and to understand the physical meaning of the solution. The simulations are provided for some of the topics. The simulations aid in the visualization of the quantum phenomenon, and for meaningful understanding of the mathematics. This approach may lead to development of "quantum mechanical intuition "as well as learning mathematical techniques for problem solving. Most importantly, the book is not flooded with numerous topics that makes the reader confused and distracted, rather the most important topics are discussed at a deeper level. The understanding of quantum mechanics is incomplete without understanding the early ideas and experiments that lead to the development of the quantum theory. Thus, the first two chapters of the book are dedicated to such topics. The key features of this book are: A simplified, structured, and step-by-step introduction to quantum mechanics. The simplification is attained through use of two-level system, step- by- step discussion of important topics in a simplified language at a deeper level, analogies, and visualization using illustrations and simulations A systematic arrangement of topics, and numerous worked- out examples. The presentation of the structure in the mathematical formalism of quantum mechanics provides clarity in understanding complicated and abstract mathematics. It also helps to understand the distinction between the quantum mechanical and classical approaches Conceptual questions at the end of every important section. The conceptual questions can be used in a classroom as a point of discussion between an instructor and students Tutorials on special topics. Simulations on special topics aid in the visualization of the physical phenomenon, and demonstration of the application of mathematics An in-depth discussion of the wave-particle duality, measurement problem, and their philosophical implications in Chapter 2 provides an understanding of the broader meaning of quantum mechanics